Rewrite as a simplified fraction. ${2.\overline{1} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 21.1111...\\ 1x &= 2.1111...\end{align*}}$ Subtracting the two equations, we have: ${9x = 19}$ ${x = \dfrac{19}{9}} \text{or} {2 \dfrac{1}{9}}$